Surface to space

Maths, computers and the internet are bringing new life, form and purpose to a traditional paper art

Most of us are familiar with the art of paper folding, perhaps as an amusing pastime with brightly coloured paper – a kind of parlour trick or children’s game. To those a bit more aware, origami has intersected with graphic design mostly as a form of three-dimensional illustration – which is one of the ways that paper folders are able to make a living. But a little investigation into the process of construction, and the developments that have occurred over the past quarter-century promise something more intriguing than a delightful puzzle. As with graphic design there is beauty in simplicity, as well as surprising complexity below the surface.

The art of paper folding can be traced back to around the seventeenth century in both European and Asian countries, but the term ‘origami’ comes from the Japanese tradition, which has a long history of folding for decorative, functional and ceremonial purposes. Origami is a version of the decorative form, which is most dominant today, where the artist is confined to working with one piece of paper and no cutting or external materials. This folding-only technique seemed to have met its limitations in possible form until the 1980s when mathematicians began to apply principles of geometry to folding patterns. Over the past tewnty years a two-way communication between mathematics and origami has evolved. Geometry helped origami artists create more accurate and complex folds, and paper folding itself has helped solve mathematical problems.

Origami has a long history of sharing of ideas: it works on a kind of open source code, and most artists are willing to share and publish their advances, discoveries and techniques. Famous in recent origami history are the ‘Bug Wars’ of the 1990s, when folding artists – most from a Japanese group known as the Origami Detectives – vied to create increasingly complex insect forms. To make a six-legged creature folded from a single sheet of paper had once been considered impossible, but since the Bug Wars, specific and detailed species of insects, crustaceans and arachnids emerged, with accurate features, as well as lifelike expression and character. As each artist shares their knowledge, the possible forms have advanced each year.

For origami, this has meant an explosion in interest, and the art has been infiltrated by scientists, theorists and artists, as well as an ever-growing hobbyist population. Many countries have large and active origami societies, and conferences are held around the world each year. Looking at the world of origami is like discovering an underground system that, unbeknown to you, has infiltrated every aspect of life, especially as folding principles are being applied to a wide range of industrial design problems, notably the packing of large surfaces into small spaces for practical applications ranging from satellites to surgery.

Like graphic notation
Different paper-folders follow different rules, setting their own boundaries. While purists will work with a single, square sheet, some will include other shapes of paper, multiple sheets, cuts, attachments and supports. What most properly defines origami is the fold. While some artists work with twisting, crumpling and the ‘wet fold’ (a soft, draping fold made with wet paper), most employ, at least in part, linear folds that become a complex mental exercise in compaction and extrusion. These folds often either begin or end with a flat plan for the origami, called a crease pattern. Crease patterns are not instructions, in that they do not lead you through step by step, but a kind of graphic notation that can be read by other origami artists, or as notes for further development by the original artist. Beautiful in themselves, the patterns provide the structure of the origami form, and they are reminiscent of complex grid systems in graphic design. Even the most whimsical forms reveal gridwork similar to that in architecture or engineering design. These defined restraints are what give origami its challenging allure. Like designers, origami artists work creatively inside linear structure.

One key figure in the Bug Wars was Robert J. Lang, (1) a California physicist who eventually left his job in 2001 to pursue origami full time; he is now one of the foremost origami artists in the world. His method of developing a design is surprising: he starts by drawing the crease pattern. Lang has the mental ability to ‘decompose’ the shape he wants to make into smaller shapes for each part. He knows the series of folds he would use for a pointed part of a certain shape, or a hooked part or a bulbous part: these are called ‘molecules’. So he will mentally calculate the molecules he needs to create each part, plug these into a square and adjust their various sizes to fit the square. Then he folds, and further adjustments follow.

One might expect the results to be coldly mechanical, but Lang’s designs are anything but, and he speaks of the ‘rush of creativity’ he gets both from making origami and from physics. Generally considered a purist, working with a single square piece of paper, his attitude on folds extends to curves, twists and even crumples; but while open to these less linear forms of shaping paper, he says that part of origami’s appeal lies in ‘the integrity of the square‚ and the elegance of the folding’, which, he says, has limitless possibilities.

Lang wrote the first computer program for designing specific origami shapes, and while he does not normally use it to design compositions, there are some complex structures he would not have been able to complete without it. He also continues to use the computer as an aid, currently working with laser-cutting to score precisely the paper, particularly for large, sculptural objects.

Paper geometry is perhaps most fully realised in origami tessellations. Tessellations are repeating patterns of the same shape – most often squares, triangles and hexagons – familiar from Islamic tilework. In origami, paper is pre-folded into grids, usually of squares or equilateral triangles, and then worked into a variety of forms, using pleats and twists along those grids. While origami tessellators often create a final piece that is geometric and repetitive in form, the technique is extremely versatile and can be used as a base for many other forms.

The American Eric Gjerde, for example, uses tessellations in a sometimes surprising combination of the technical and the quirky. (2) If a sense of humour can be evident in mathematics, it is realised in Gjerde’s more imaginative forms, such as the strange, geometric sea-cucumber shape he calls ‘Night Crawler’. Despite that piece’s creature-like form, Gjerde says he finds himself heading more towards the abstract and geometric, while also searching for organic and chaotic elements to introduce a natural element into what he is creating. His process is exploratory, and he will play with a fold and make discoveries along the way. He keeps these ‘work sketches’ in a set of boxes for future reference.

‘I have a stack of boxes full of things that look like fragments from an Escheresque nightmare. Sometimes when I’m all out of ideas I take one of these boxes and up-end it onto my work table and scatter the bits about – like throwing bones, I suppose. Occasionally something takes shape from the fragments and I find myself quite pleased with the results; other times I just end up tossing the whole lot into the bin. I’m quite fascinated with structure and with surfaces; that, I think, puts me in a slightly different place to many origami creators. I’ve never been interested in creating physical representations of objects; instead I’m rather obsessed with patterns and morphological topologies.’

Still in the land of geometry, there is a subgroup of ‘modular origami’, where multiple pieces of the same shape are connected together, often in a kind of quilt, or a complex geometric solid. Robert J. Lang also excels at this, using multiple strips and an extended list of rules (itemised on his website). He calls these structures ‘polypolyhedra’, though they are also known as ‘orderly tangles’‚ or ‘knotwork’. Calling to mind those wooden or metal puzzles that one is challenged to pull apart and / or reassemble, they are hard to get your head around in any sense, let alone as folded forms.

Renaissance men
Canadian Joseph Wu, (3) another of the few full-time origami artists, says we are currently in a ‘renaissance’ of origami, where a former rivalry between the mathematical purists and the ‘pure artists’ has settled into an easier trade of respect and information. He counts himself among the latter group in his own quest for expression in form. Like Lang, he prefers to use only one square, but likens his process more to what psychologists call ‘thin-slicing’ (making sense of situations based on the thinnest slice of experience (4)). He says, ‘When I decide on a subject, I do some fairly extensive research in order to familiarise myself with the details. Once I am ready, the thin-slicing kicks in. In less than a minute, I have a finished design in my head. It’s not in a describable form at that point, just a holistic design. I know that there is a path from the unfolded paper to the finished product. After that, I need to work it out by folding it. Until that first attempt is made, I cannot describe the design in any way. The first attempt is usually about 90 per cent of the way to the finished design. I then do five to ten iterations to work out the fine details.’ More than technically correct, Joseph’s pieces have an intuitive naturalness and sculptural quality to them.

A terrific example of how the mathematical principles have led to the advancements in artistic form can be seen in the work of Eric Joisel, (5) from France. His extremely complex humanoid forms show the underlying structure of the tessellating pleat intersections combined with other folding styles and soft crumples. He is a star in the origami world, and the fact that his fantastical figures are still made from a single folded sheet demonstrates a startling level of virtuosity.

Delegates at origami conferences also look forward to the appearance of the Belgian artist Herman van Goubergen, as he is known for creating a single new technique each year, then presenting – in essence releasing it. Once he has revealed his yearly discovery, he leaves it to others to build on and incorporate the technique into their own designs. His ‘curler units’ are now widely used to attach multiple pieces together; in 2006 he used a mirror to reveal out-of-sight folds to make the sculpture complete, and lately he has been working on motion, realised in a rolling toy car and rows of ‘floating’ ducks.

Flatland
Strangely, few origami artists seem to exploit existing graphics on paper, apart from those who fold money, often incorporating the patterns on the note into their designs. Money folding is practised in all countries with paper money, though the American dollar bill is favoured for its 3 x 7 proportions. Hawaiian Won Park (6) has made a number of models that use specific parts of the printed design for the folded object, but even he says that most of the time ‘paper is paper’.

Then there is the ‘Two Fold Santa’ by Paula Versnick, (7) from Holland. The Santa is designed to make a flat representation rather than a three-dimensional one. The brilliance is in its simplicity: the paper is used as shape and colour, and a reductive visualisation of paper folds to a graphic end. Versnick calls her approach ‘doodling’. She folds and maybe there is nothing, she makes another fold and maybe there is something, yet another fold, and something appears. The ‘Two-Fold Santa’ was found this way in 2001, and has since been accompanied by simple scenery (eleven folds in four square pieces). She says: ‘I like the concept of folding something that only shows the essence. The simplest designs start out with a doodle, but I try to pay attention . . . and I try to open my mind while doodling. I start with a fold that is not obvious. I look at the paper closely, to figure out from the beginning if it leads me to something.’

She enjoys the element of surprise, when at first the folds seem meaningless, but the last one reveals the ‘Aha!’ moment. She is particularly happy with a four-fold heart of which she says: ‘The fun of this heart is that when you make the first two folds, you only create two coloured rectangles on opposite sides of the paper. And then you have to turn the paper around and bring the rectangles together . . . Surprise! It’s a heart.’

The basic structures of folding relate to the structures of maths: fractals, tessellations and repeating patterns occur in nature, and as origami becomes increasingly complex it is possible to imagine the many forms it could take. Grids, structure, planning, shape, form, colour, paper. The materials, combined structure and creativity and logical but intuitive approach to visual expression share much with graphic design. To create a paper sculpture is one thing, to create a complex shape from a single piece of paper is another, more fascinating thing, but to create shape and form from a single flat sheet with an identifiable, mappable structure is where origami begins to trigger some very familiar nodes in the designer’s brain. As with design, there is a relationship between elegant simplicity and creative form, and it is the controlled structure that serves to unlock so many possibilities. Rather than pure expression, it may be the restraints – both self-imposed and inherent – that make origami so compelling.

First published in Eye no. 67 vol. 17 2008

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